There are many situations requiring verification of an elongated part (“rigid transport element”) whose cross-sectional shape varies along its length. For example, water pipes in buildings, pneumatic tubing in machinery, and tubing carrying fluids and liquids in aircraft, may all change in shape along the length of the part. In certain applications, such as applications relevant to the aerospace industry, tubing may be required to be placed in different areas of an aircraft, for example, that impose widely varying and severe constraints on the shape of the tubing. A consequence of a changing cross-sectional shape of a rigid transport element is a variation in the maximum amount of liquid that can flow through the element, or a variation in the pressure of a gas that flows through the element. In order to ensure that a rigid transport element is satisfactory for intended uses, an engineer or other personnel must verify the rigid transport element by conducting analyses, checking, for example, that pressure changes of fluids flowing through the rigid transport element do not exceed tolerances.
In order to verify the rigid transport element, particular cross-sections of the tubing must be located and analyzed, and characteristics or those cross-sections, such as area, shape, and position relative to adjacent cross-sections must be determined. The cross-sections that must be located and analyzed are called analytical transitional cross-sections. Referring to FIGS. 1A and 1B, an example of a rigid transport element 200 is shown. FIG. 1A shows a representation of the rigid transport element 200 and FIG. 1B shows all analytical transitional cross sections 201-204 of the element 200.
Previously, location of these analytical transitional cross-sections had been done in a non-automated fashion, by an operator using a three dimensional Computer Aided Design (3D CAD) system. Prior to verification, a 3D CAD model of the rigid transport element to be tested would be created by a design engineer or other operator in a 3D CAD environment. The 3D CAD model would be saved to a non-volatile memory location such as a hard disk. A verification engineer or other similar operator would load the 3D CAD model of the rigid transport element to analyze and verify that the design of the element meets technical requirements. Verification would consist of manually determining the locations of the analytical transitional cross-sections. Each analytical transitional cross-section would then be analyzed for perimeter, radius, area, axis length and shape between two cross-sections, bend angle, and total length of the rigid transport element, as well as other features.
One problem with any manual procedure is that it is very time consuming since each model must be manually analyzed. A further problem is that manual analysis subjects the verification procedure to human error. A further problem is that a manual analysis does not allow for complete automation of the fluid dynamics analysis procedure.
Therefore, there is a need for an automated method of determining the analytical transitional cross-sections of a rigid transport element.
Disclosure of such an automated method requires understanding of some basic features of 3D CAD systems. Generally, 3D CAD systems allow an operator to create a computer representation (a model) of a three dimensional object. A 3D model is stored in a computer as a collection of “primitive elements.” These primitive elements may be of several types, such as edges, faces, and points. Edges are connected to each other at points. A 3D structure is defined by its “boundary representation,” or the collection of border objects that demarcate the space occupied by the 3D object. As an example of a full 3D model, the boundary representation for a square consists of 4 edges, 4 points, and a face. The boundary representation of a cube would consist of 8 edges and 8 points and six faces. A structure of a cylinder is defined by circular boundary cross-sections and cylindrical faces.
For further illustration of CAD features, reference is now made to FIG. 2. A model of a rigid transport element 10 is generally comprised of pseudo-cylindrical faces 51-52, and 91-96, cross-sections 20, 60 and 100, and longitudinal edges 41-42 and 81-86. The first end 20 of the model 10 is circular, which in a 3D CAD representation, is usually composed of two semi-circular edges 21-22, each with two end-points 31-32.
This model 10 consists of a circle 20, longitudinally connected to another circle 60, longitudinally connected to a rectangle 100. We will call the portion of the model between the two circles 20 and 60 a first “segment” 40 and the portion of the model between the second circle 60 and the rectangle 100 a second “segment” 80.
In the first segment 40, there are two longitudinal edges 41-42 which divide up the segment 40 into two semi-cylindrical faces 51-52. The boundary representation of face 51 comprises semi-circular edge 22, longitudinal edges 41-42 and arc-edges 62-64 (the circle 60 is comprised of 6 edges, rather than 2, because of the fact that it is connected with a rectangle 100). In the second segment 80, there are 6 longitudinal edges 81-86, defining 6 faces 91-96 and connected to cross-sections 60 and 100. The foregoing example provides illustration of some features present in 3D CAD systems. Additional definitions of terms used in this disclosure are as follows:
Rigid Transport Element: a 3D conduit structure, such as a hollow elongated element that can carry fluid.
List: a data structure into which elements may be placed, and out of which elements may be moved, copied or deleted.
Primitive Element: a basic element out of which CAD models are formed.
Edge or Topological Edge: an edge is a primitive curved or straight line element that follows a particular path and can be used to define a two or three dimensional object.
Face or Topological Face: a face is a primitive surface element which can be used to define a three dimensional object.
Analytical transitional cross-section or Analytical Cross-Section: a cross-section of a rigid transport element which is used to calculate diagnostic characteristics of the rigid transport element.
Connectivity: for one edge to have connectivity with another edge means that an edge shares an endpoint with another edge.
Planar intersectional curve: a 2D curve formed by intersecting a 3D surface with a plane. A planar intersectional cross-section curve is a 2D curve formed by intersecting a 3D surface of a hollow object such as a rigid transport element with a plane at a cross-section of the hollow object.